OFFSET
0,3
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).
FORMULA
G.f.: (1 + x^2 + x^3 + x^4)/((1 + x)*(1 + x + x^2)*(1 - x)^3).
a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).
a(n) = 1 + floor(n/2 + n^2/3).
a(n) = (12*n^2 + 18*n + 4*(-1)^(2*n/3) + 4*(-1)^(-2*n/3) + 9*(-1)^n + 19)/36.
a(n) - n = a(-n).
a(6*k+r) = 12*k^2 + (4*r+3)*k + a(r), where 0 <= r <= 5. Particular cases:
a(n+2) - a(n) = A004773(n+2).
a(n+3) - a(n) = A014601(n+2).
a(n+4) - a(n) = A047480(n+3).
a(n) - a(-n+3) = 2*A001651(n-1).
a(n) + a(-n+3) = 2*A097922(n-1).
MAPLE
A281333:=n->1 + floor(n/2) + floor(n^2/3): seq(A281333(n), n=0..100); # Wesley Ivan Hurt, Feb 09 2017
MATHEMATICA
Table[1 + Floor[n/2] + Floor[n^2/3], {n, 0, 60}]
LinearRecurrence[{1, 1, 0, -1, -1, 1}, {1, 1, 3, 5, 8, 11}, 80] (* Harvey P. Dale, Sep 29 2024 *)
PROG
(PARI) vector(60, n, n--; 1+floor(n/2)+floor(n^2/3))
(Python) [1+int(n/2)+int(n**2/3) for n in range(60)]
(Sage) [1+floor(n/2)+floor(n^2/3) for n in range(60)]
(Maxima) makelist(1+floor(n/2)+floor(n^2/3), n, 0, 60);
(Magma) [1 + n div 2 + n^2 div 3: n in [0..60]];
CROSSREFS
Cf. A236771: n + floor(n/2) + floor(n^2/3).
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jan 20 2017
STATUS
approved